<p>Data-driven event-triggered control has been widely studied for linear systems, yet its extension to switched systems, typically leads to asynchronous switching between controllers and its corresponding subsystems. This paper develops a direct data-driven control strategy for continuous-time switched linear systems subject to the event-triggering-induced asynchronous switching, covering both disturbance-free and disturbed cases. First, a novel data-based characterization of the controller-subsystem asynchrony is introduced. Second, the event-triggered mechanism and feedback control gains are co-designed via data-based linear matrix inequalities, which are independent of any precise system model. Then, sufficient conditions are established for the practical exponential stabilization of the resulting closed-loop switched linear systems. These criteria can be deduced to linear systems. In contrast to the existing work, this paper offers a straightforward mechanism to preclude Zeno behavior, allowing for the explicit computation of a minimum inter-event time. The effectiveness of the proposed results is finally verified through two comparative examples.</p>